We study direct load control contracts that utilities use to curtail customers’ electricity consumption during peak-load periods. These contracts place limits on the number of calls and total number of hours of power reduction per customer per year as well as the duration of each call. The stochastic dynamic program that determines how many customers to call and the timing and duration of each call for each day is an extremely difficult (NP-hard) optimization problem. We design a scenario-based approximation method to generate probabilistic allocation polices in a reasonable amount of time. Our approach consists of three approximations: deterministic approximation of demand, discretization of the expected demand, and aggregation/disaggregation of the resources. We show the relative information error resulting from the deterministic approximation is O(1=√+ n), the discretization error is O(1=n), and the aggregation/disaggregation error is O(1=n), where n represents the length of the horizon. Finally, we show the total relative error is O(1=√+n). Our error analysis establishes that our approximation method is near optimal. In addition, our extensive numerical experiments verify the high quality of our approximation approach. The error, conservatively measured, is quite small and has an average and standard deviation of 8.6% and 1.4%, respectively. We apply our solution approach to the data provided by three major utility companies in California. Overall, our study shows our procedure improves the savings in energy-generation cost by 37.7% relative to current practices.
Fattahi, A., Dasu, S., & Ahmadi, R. (2023). Peak-Load Energy Management by Direct Load Control Contracts. Management Science, 69(5), 2788–2813. https://doi.org/10.1287/mnsc.2022.4493